On Dominator Colorings in Graphs
نویسنده
چکیده
Given a graph G, the dominator coloring problem seeks a proper coloring of G with the additional property that every vertex in the graph dominates an entire color class. We seek to minimize the number of color classes. We study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also show the relation between dominator chromatic number, chromatic number, and domination number.
منابع مشابه
Algorithmic Aspects of Dominator Colorings in Graphs
In this paper we initiate a systematic study of a problem that has the flavor of two classical problems, namely Coloring and Domination, from the perspective of algorithms and complexity. A dominator coloring of a graph G is an assignment of colors to the vertices of G such that it is a proper coloring and every vertex dominates all the vertices of at least one color class. The minimum number o...
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J. A. Bondy and U. S. R. Murty, Graph theory with Applications, London: MacMillan (1976). R. M. Gera, On Dominator Colorings in Graphs, Graph Theory Notes of New York LIT, 25-30 (2007) F. Harary, Graph Theory, Narosa Publishing 1969. D. Michalak, On Middle and Total graphs with Coarseness Number Equal 1, Lecture Notes in Mathematics, Volume 1018: Graph Theory, Springer-Verlag, Berlin, 139 – 150...
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